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If x^2+y^2=25xy. then prove that 2log(x+...

If `x^2+y^2=25xy.` then prove that `2log(x+y)=3log3+logx+logy.`

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VGS PUBLICATION-BRILLIANT-REAL NUMBERS-EXERCISE
  1. Expand the following. log((p^2q^3)/r^4)

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  2. Expand the following. (v) log sqrt((x^3)/(y^2))

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  3. If x^2+y^2=25xy. then prove that 2log(x+y)=3log3+logx+logy.

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  4. If log((x+y)/(3))=1/2(logx+logy), then find the values of (x)/(y)+(y)/...

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  5. If (2.3)^x=(0.23)^y=1000 then find the value of (1)/(x)-(1)/(y).

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  6. If 2^(x+1)=3^(1-x) then find the value of x.

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  7. Is (i) log 2 is rational or irrational ? Justify your answer.

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  8. Is (ii) log 100 is rational or irrational ? Justify your answer.

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  9. Can the number 6^n, n being a natural number, end with the digit 5 ? G...

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  10. Is 7xx5xx3xx2+3 a composite number ? Justify your answer.

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  11. Prove that (2sqrt3+sqrt5) is an irrational number. Also check whether ...

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  12. If x^2 + y^2 = 6xy , prove that 2 log (x + y) = logx + logy + 3 log 2

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  13. Find the number of digit in 4^(2013), if log(10)2=0.3010.

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  14. Insert 4 rational numbers between 3/4 and 1 without using (a+b)/(2) fo...

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  15. If the prime factorization of a natural number (n) is 2^2xx3^2xx5^2xx7...

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  16. Find the value of log(5)125.

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  17. Write any two irrational numbers lying between 3 and 4.

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  18. Find the value of log(sqrt2) 256.

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  19. Find the HCF and LCM of 90, 144 by prime factorisation method.

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  20. Is log3 81 rational or irrational ? Justify your answer.

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